A recursive construction for projective Reed-Muller codes
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929584394469376 |
|---|---|
| author | San-José, Rodrigo |
| author_facet | San-José, Rodrigo |
| contents | We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of projective Reed-Muller codes for some particular degrees that give codes with good parameters. Moreover, from this recursive construction we derive a lower bound for the generalized Hamming weights of projective Reed-Muller codes which is sharp in most of the cases we have checked. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05072 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A recursive construction for projective Reed-Muller codes San-José, Rodrigo Information Theory Commutative Algebra 94B05 (Primary) 11T71, 14G50 (Secondary) We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of projective Reed-Muller codes for some particular degrees that give codes with good parameters. Moreover, from this recursive construction we derive a lower bound for the generalized Hamming weights of projective Reed-Muller codes which is sharp in most of the cases we have checked. |
| title | A recursive construction for projective Reed-Muller codes |
| topic | Information Theory Commutative Algebra 94B05 (Primary) 11T71, 14G50 (Secondary) |
| url | https://arxiv.org/abs/2312.05072 |